These Tablets Aren't For Your Heartburn

Last night was quite the bamboozler. I went to a Secret Science Club (probably shouldn't have told you that) meeting in Brooklyn. The speaker was Tony Rothman, a Cosmologist and Physics professor at Princeton. He talked about San Gaku's which are old Japanese mathematical tablets. On them were ancient geometical problems like this one:


Here is the solution

Considering there are only about 900 that remain of these, I don't think they are going to replace Sudoku's anytime soon (althought they should). Rothman also wrote a book this year called Sacred Mathematics: Japenese Temple Geometry. He was selling signed copies there, but I was too busy getting my flirt on with some scientific honeys, and they sold out. Overall, the meeting was a good time. I'll end with a cool puzzler that was asked at the beginning.

Three mathematicians are talking.
"How many kids do you have?" The first asks the second mathematician.
"Three," she answers.
"How old are they?" he asks.
"Well if you multiply their ages, you get 72. But if you add them, you get
your office number." She says.

The first mathematician thinks for a few seconds and says, "I do not think
there is enough information for me to solve this!" he says.

The mother mathematician immediately says, "Oh, of course, I forgot to tell
you that the eldest plays the violin!"


What are the ages of the children???

Answer